Use the angle subtraction formula for cosine.

Q.2 (i) Find the value of $\cos 15^\circ$.

Step 1: Use the angle subtraction formula for cosine.

$$\cos(A - B) = \cos A \cos B + \sin A \sin B$$

Let $A = 45^\circ$ and $B = 30^\circ$.

Step 2: Substitute the values of $A$ and $B$.

$$\cos 15^\circ = \cos(45^\circ - 30^\circ) = \cos 45^\circ \cos 30^\circ + \sin 45^\circ \sin 30^\circ$$

Step 3: Substitute the known trigonometric values.

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